• Patient has provided written informed consent.

• Male patients must be 18 years of age or older at the time of written informed consent.

• Histologically or cytologically confirmed adenocarcinoma of the prostate, OR unequivocal diagnosis of metastatic prostate cancer (i.e., involving bone or pelvic lymph nodes or para-aortic lymph nodes) with an elevated serum prostate specific antigen (PSA).

• Eastern Cooperative Oncology Group (ECOG) performance status ≤ 2.

• Patients must have had prior treatment with at least one line of taxane chemotherapy, unless medically unsuitable.

• Patients must have had prior treatment with at least one second-generation androgen receptor (AR)-targeted agent (e.g., enzalutamide, abiraterone, apalutamide or darolutamide).

• Patients must have progressive disease defined according to The Prostate Cancer Clinical Trials Working Group 3 (PCWG3) as any one of the following:

∙ PSA progression - minimum of 2 rising PSA values from a baseline measurement with an interval of ≥ 1 week between each measurement

‣ Soft tissue progression as per Response Evaluation Criteria in Solid Tumours version 1.1 (RECIST 1.1) criteria

‣ Bone progression: ≥ 2 new lesions on bone scan

• Prior surgical orchiectomy or chemical castration maintained on luteinizing hormone-releasing hormone (LHRH) analogue (agonist or antagonist).

• Serum testosterone levels ≤ 1.75nmol/L (≤ 50ng/dL).

⁃ Significant prostate specific membrane antigen (PSMA) avidity on PSMA positron emission tomography (PET)/computed tomography (CT), defined as a minimum uptake of maximum standardised uptake value (SUVmax) 20 at a site of disease, and SUVmax \> 10 at sites of measurable soft tissue disease ≥ 15mm (unless subject to factors explaining a lower uptake, e.g. respiratory motion, reconstruction artefact).

⁃ Patients must have a life expectancy ≥ 6 months.

⁃ Patients must have adequate bone marrow, hepatic and renal function, defined as:

• Haemoglobin ≥ 100g/L independent of transfusions (no red blood cell transfusion in last 4 weeks)

∙ Absolute neutrophil count (ANC) ≥ 1.5 x 10\^9/L

∙ Platelets ≥ 150 x 10\^9/L

∙ Total bilirubin ≤ 1.5x upper limit of normal (ULN) except for patients with known Gilbert's syndrome, where this applies for the unconjugated bilirubin component

∙ Aspartate transaminase (AST) and alanine transaminase (ALT) ≤ 3x ULN if there is no evidence of liver metastasis or ≤ 5x ULN in the presence of liver metastases

∙ Adequate renal function: patients must have a creatinine clearance estimated of ≥ 40mL/min using the Cockcroft Gault equation (Appendix 3)

⁃ Sexually active patients are willing to use medically acceptable forms of barrier contraception.

⁃ Willing and able to comply with all study requirements, including all treatments and the timing and nature of all required assessments.

⁃ At least 3 weeks since the completion of surgery or radiotherapy prior to registration.